Abstract:

           Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material etc., Hence, it is needed to develop inventory models with random replenishment. In this paper we develop and analyze an inventory model with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalized Pareto distribution and demand is a function of selling price. The instantaneous level of inventory at any given time ‘t’ is derived through differential equations. With suitable cost considerations the optimal ordering and pricing policies are obtained. The sensitivity analysis of the model reveals that the random replenishment has a significance influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.

Keywords: Random replenishment, generalized Pareto decay, selling price demand, EPQ model, Weibull distribution.